Optical switch

ABSTRACT

An optical switch uses a polarisation insensitive spatial light modulator operation by a double pass through a liquid crystal cell. The switch includes two such modulators in a cross bar arrangement. Different embodiments employing techniques for reducing cross talk are described.

FIELD OF THE INVENTION

The invention relates to the general field of optical switching and moreparticularly to optical switching using multiphase or continuous phasehologram devices.

BACKGROUND OF THE INVENTION

Optical fibre switching components are fundamental to modern globalinformation systems. Single-stage matrix switches operatingindependently of the optical bit-rate and modulation formats, capable ofreconfigurably interconnecting N optical inputs to M optical outputs(where N and M are generally, but not necessarily the same number), areparticularly attractive. Many switches for achieving the requiredswitching are limited in functional size to less than 64×64, and/orsuffer from relatively poor noise performance. One method which providesgood noise performance and is potentially more scalable than otheroptical switch technologies is to use reconfigurable holograms aselements for deflecting optical beams between arrays of optical inputsand optical outputs.

A known holographic optical switch, otherwise known as an opticalshuffle, is shown in FIG. 1.

In FIG. 1, an array of optical sources 1 and an array of opticalreceivers 7 are arranged as the inputs and outputs of a holographicswitch. For many applications, the sources and receivers may comprisecleaved or end-polished fibres. In other applications, the inputs may belight emitting sources such as lasers or LEDs, and the outputs may bephoto-detectors. Each input 1 may transmit a different digital or analogoptical signal through the switch to one (or possibly several) of theoutputs 7. Thus up to N different inputs may be simultaneously passingthrough the switch at any instant. Each input may consist of asingle-wavelength modulated by data; a number of different data sourcesoperating at different wavelengths (e.g. a wavelength-multiplexedsystem); or a continuum of wavelengths. Although the switch is shown incross-section in FIG. 1, the input & output arrays 1, 7 are typically2-dimensional arrays, and the holographic switch occupies a3-dimensional volume.

To achieve switching, the input array 1 is arranged behind a first lensarray 2. Each optical signal emitted by the input array entersfree-space, where it is collimated by one of the lenses in first lensarray 2. Each collimated beam then passes through a first hologramdisplay device 3. The first hologram display device 3 displays aholographic pattern of phase and/or intensity and/or birefringence whichhas been designed to produce a specific deflection of the opticalpropagation directions of the beams incident upon the device. Thehologram pattern may also be designed such that each optical beamexperiences a different angle of deflection. The first hologram displaydevice 3 may also have the effect of splitting an individual beam intoseveral different angles or diffraction orders. One application forutilising this power splitting effect is to route an input port to morethan one output port.

The deflected optical signals propagate in free-space across aninterconnect region 4 until they reach a second hologram device 5. Thehologram pattern at second hologram device 5 is designed in such a wayto reverse the deflections introduced at the first hologram displaydevice 3 so that the emerging signal beams are parallel with the systemoptic axis again.

The optical signals then pass through a second lens array 6 where eachlens focuses its associated optical signal into the output ports of areceiver array 7. Thus the hologram pattern displayed on first hologramdisplay device 3 and the associated “inverse” hologram pattern displayedon second hologram display device 5 determine which output fibre orfibres 7 receive optical data from which input fibre or fibres 1. Theinterconnect region 4 allows the signal beams to spatially reorder in amanner determined by the specific hologram patterns displayed on thefirst 3 and second 5 hologram display devices. The switch also operatesreversibly such that outputs 7 may transmit optical signals back to theinputs 1.

The system shown in FIG. 1 (and functionally equivalent configurationsutilising planes of symmetry within the switch optics) is well known asa method for static optical shuffle, using fixed hologram recordings asfirst 3 and second 5 hologram display devices whereby the input signalsare “hard-wired” to specific outputs.

It has been proposed to extend the optical shuffle of FIG. 1 to providea reconfigurable switch by displaying hologram patterns on a spatiallight modulator (SLM). There are however a number of practical designproblems associated with the migration from a static optical shuffle toa reconfigurable switch. Among these are the following:

-   -   1) Known SLMs, using a ferroelectric liquid crystal provide        binary phase modulation and such phase modulation can be    -   2) polarisation-insensitive. However, the maximum theoretical        diffraction efficiency for a binary phase device is only 40.5%.        For example, the architecture shown in FIG. 1 uses two SLM        devices, and hence the maximum net diffraction efficiency of        this system is 16.4%. The diffraction efficiency of holographic        system would be improved significantly by using multiple phase        modulation. For many applications this multiple phase modulation        must be polarisation-insensitive. It is desirable that the phase        may be varied continuously between 0 and (at least) 2π.    -   3) In order to implement a holographic switch using two SLMs, an        appropriate set of hologram patterns must be chosen. This        hologram set must be capable of routing any input channel to any        input channel whilst keeping the crosstalk figures within        specified values. In particular, the hologram set must be        optimised to prevent beams associated with unwanted diffraction        orders from being launched down the wrong channel. Increasing        the number of phase levels tends to result in a decrease in the        strength of the unwanted diffraction orders.    -   4) A convenient method of constructing reconfigurable holograms        for use within an N×N switch would be to integrate a layer of        liquid crystal material above a silicon circuit. This type of        SLM typically operates in reflection rather than transmission,        and the switch layout shown in FIG. 1 is therefore no longer        appropriate.

Accordingly the present invention aims to address at least some of theseissues.

SUMMERY OF THE INVENTION

According to a first aspect of the invention there is provided a switchcomprising an integrated spatial light modulator for receiving light ofa predetermined wavelength, the modulator comprising a liquid crystallayer spaced from a second layer by a layer having an optical retardanceof an odd integer number of quarter-waves of said wavelength, whereinthe second layer is reflective of said light of said wavelength.

In one embodiment said liquid crystal layer is a nematic crystal layer.

In another said liquid crystal layer is a π-cell.

Preferably the second layer is a metallic layer.

Advantageously the metallic layer is of Aluminium.

Conveniently said wavelength is 1.57 μm

According to a second aspect of the invention there is provided a switchcomprising an integrated spatial light modulator for receiving light ofa predetermined wavelength, the modulator comprising a liquid crystalcell having a pair of opposed and mutually substantially parallel endplates disposed substantially parallel to an axial plane, and spacedapart by a liquid crystal layer providing a director angle tilt in atilt plane substantially orthogonal to said axial plane, said liquidcrystal being spaced from a second layer by an optical layer having aretardance of an odd integer number of quarter-waves of said wavelength,wherein the second layer is reflective of said light of said wavelength,and the optical layer being disposed with respect to said tilt planesuch that light polarised in said tilt plane returns through said liquidcrystal layer polarised substantially orthogonal to said tilt plane.

Preferably said liquid crystal layer is a nematic crystal layer.

Alternatively said liquid crystal layer is a π-cell.

Preferably the second layer is a metallic layer.

Conveniently the metallic layer is of Aluminium.

Advantageously the modulator has a glass cover disposed over said liquidcrystal layer, and the metallic layer has a connection to drivingcircuitry for switching the modulator.

According to another aspect of the invention there is provided a methodof switching a light beam having a first component polarised in a firstdirection and a second component polarised in a second directionorthogonal to the first, the method comprising providing a device havinga liquid crystal layer and an optical retardance, the liquid crystalbeing responsive to a variable drive voltage to provide a correspondingvariation in director angle tilt; and further comprising: applying avariable drive voltage to said liquid crystal device; applying said beamto said liquid crystal device to provide an intermediate beam having avariable phase delay applied to said first component and an at leastsubstantially fixed phase delay to said second component; by saidretardance, rotating the polarisation of said intermediate beam;applying the resultant light to said liquid crystal device whereby acomponent of said resultant light polarised in said first directionreceives said variable phase delay and a component of said resultantlight polarised in said second direction receives said at leastsubstantially fixed phase delay.

Preferably the rotating step comprises rotating said polarisationthrough 90 degrees whereby at least substantially equal amounts ofvariable phase delay are applied to each of said first and secondcomponents.

Advantageously the rotating step comprises a step of reflecting saidintermediate beam back along its incoming path.

According to yet another aspect of the invention there is provided anoptical switch comprising a plurality of input optical fibres forproviding plural input light beams, a plurality of optical receivers forreceiving output light beams, a first and a second reflective spatiallight modulator, and drive circuitry for forming a respective pluralityof switching holograms on each spatial light modulator, said hologramsbeing selected to couple each said input optical source to a respectivedesired optical receiver, wherein each spatial light modulatorincorporates a liquid crystal device for modulating the phase of lighttravelling through said liquid crystal device, a reflector device forreturning light back through said liquid crystal device and a device,disposed between said liquid crystal device and said reflector device,for rotating the polarisation of light by 90 degrees, wherein theoptical switch has an axis of symmetry and the spatial light modulatorsare disposed on opposite sides of said axis, each said switchinghologram on said first spatial light modulator being operative todeflect said input light beams to said switching holograms on saidsecond spatial light modulator and each said switching hologram on saidsecond spatial light modulator being operative to deflect said lightbeams to a respective optical receiver.

Preferably each said input optical fibre is directed towards arespective switching hologram on said first spatial light modulator, andeach said optical receiver comprises an output optical fibre, whereineach output optical fibre is directed towards a respective switchinghologram on said second spatial light modulator.

In one embodiment the first and second spatial light modulators aredisposed such that a respective zero-order beam reflected from eachswitching hologram on said first spatial light modulator is incident ona respective switching hologram on said second spatial light modulator.

Preferably a half wave plate is disposed between said first and secondspatial light modulators.

Alternatively the switching holograms are spaced apart on said first andsecond spatial light modulators and the first and second spatial lightmodulators are disposed such that a respective zero-order beam reflectedfrom each switching hologram on said first spatial light modulator isincident on a spacing between two adjacent switching holograms on saidsecond spatial light modulator.

Advantageously a half wave plate is disposed between said first andsecond spatial light modulators.

Conveniently the switch further comprises respective optical systemsdisposed between said input fibres and said first spatial lightmodulator and between said output fibres and said second spatial lightmodulator, wherein each said optical system comprises two confocallenses, the input and output fibres being disposed in respective planesand a focal plane of a first lens of each optical system coinciding withthe plane of the associated fibres.

Preferably the input and output fibres are disposed in respective planesand the optical switch further comprises respective arrays ofmicrolenses, said microlenses being disposed in front of each fibreplane such that each microlens corresponds to a respective fibre, andrespective optical systems disposed between said input fibres and saidfirst spatial light modulator and between said output fibres and saidsecond spatial light modulator, wherein each said optical systemcomprises two confocal lenses, and a focal plane of a first lens of eachoptical system coinciding with the output focal plane of the associatedmicrolens array.

Advantageously said optical fibres are thermally expanded core (TEC)fibres.

In another embodiment the first and second spatial light modulators aremutually offset so that no zero order beams from the first spatial lightmodulator is incident on the second spatial light modulator.

Conveniently at least one optical receiving element is disposed in aregion receiving said zero-order beams from said first spatial lightmodulator, whereby input signal may be monitored.

Advantageously, the or each element is a fibre. Alternatively otherelements such as receiver diodes could be used.

Preferably each switching hologram provides a repeating pattern on itsspatial light modulator, whereby the repeating patterns on the two SLMssatisfy the relation:θ₂(u)=θ₁(−u)where θ₂(u) is the repeating pattern on the second SLM and θ₁(−u) is therepeating pattern on the first SLM, and the angle of incidence is suchthat the Poynting vector of the input light beam incident on the firstSLM, and of the light beams leaving the second SLM, is in the plane oftilt of the director.

In a preferred embodiment, the output fibres are secured together in anarray by a glue containing black pigment to attenuate misaligned light.

In another preferred embodiment, the output fibres are secured togetherto form an array and the spacing between the fibres of the array isoccupied by interstitial fibres which serve to accept and guide awaycross talk from the switching zone.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting embodiments of the invention will now be described withreference to the accompanying drawings, in which:

FIG. 1 shows a prior art optical switch useful in understanding thepresent invention;

FIG. 2 is a schematic diagram showing the propagation of a planar wavefront through a uniaxial liquid crystal device;

FIG. 3 shows the use of a quarter-wave plate, and illustrates thepolarisation states of an input field in a double-pass reflectivesystem;

FIG. 4 shows a schematic cross-sectional view of a first embodiment of aSLM with integral quarter-wave plate;

FIG. 5 shows a schematic cross-sectional view of a second embodiment ofa SLM with integral quarter-wave plate;

FIG. 6 shows an overview of an exemplary silicon back plate layout forthe device of FIG. 5;

FIG. 7 shows a schematic diagram of a pi cell for use in the invention;

FIG. 8 shows a partial layout diagram of a first embodiment of anoptical switch using two reflective SLMs, in accordance with theinvention;

FIG. 9 shows a schematic diagram of a part of a first optical systemuseable in the switch of FIG. 8;

FIG. 10 shows a schematic diagram of a part of a second optical systemincluding a microlens array, useable in the switch of FIG. 8;

FIG. 11 shows the effects of zero-order cross talk in the device of FIG.8;

FIG. 12 shows a partial layout diagram of a second embodiment of anoptical switch in accordance with the invention, being a modification ofFIG. 8 to include a half wave plate in the optical path between the twoSLMs;

FIG. 13 shows a partial layout diagram of a third embodiment of anoptical switch in accordance with the invention, being a modification ofFIG. 8 having the output SLM offset laterally to reduce cross talk.

FIG. 14 shows a fourth embodiment in which the output SLM is offsettransversally to avoid cross talk;

FIG. 15 shows propagation conditions inside the liquid crystal; and

FIG. 16 shows the differing propagation conditions inside the input andoutput SLMs.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the various figures, like reference signs indicate like parts.

FIG. 2 shows the propagation of a planar wave front 100, travellingalong the z-direction through a layer of uniaxial liquid crystal cell101 of uniform alignment. The cell comprises a front plate 102 and arear plate 103 sandwiching the liquid crystal 104. The optical axis 105,later also referred to herein as a director axis of the uniaxial mediumhas been taken in the general case to tilt away from the x-direction byan angle θ on to the plane xOz. The tilt angle θ is electricallycontrollable by a voltage applied across the liquid crystal cell 101.The two propagation modes travel along the z-direction with differentvelocities: these may be calculated using a geometric construction inwhich an ellipsoid is drawn with a long axis of length n_(θ)parallel tothe director. For a uniaxial medium the other two axes of the ellipsoidhave equal lengths (n₀). A plane is constructed perpendicular to thePoynting vector (in this case the plane is parallel to the xOy plane).The intersection of this plane with the ellipsoid defines an ellipse110. The directions of the major and minor axes 111, 112 of this ellipsedefine the two orthogonal polarisation modes, while the lengths of thesetwo axes define the refractive index experienced by the correspondingmode. For a tilt in the xOz plane, the minor axis of this ellipse isparallel to the y direction, and the major axis is therefore parallel tothe x direction, for all values of θ. Hence, for any θ, the x and ydirections are parallel to the polarisation modes, so that thecomponents of incident light polarised in these directions will remainin these directions on propagation through the liquid crystal. Thisremains true even if the tilt angle θ is changing inside the medium.

The length of the minor axis 112 is n₀, for all values of θ. Hence thecomponent of the field that is parallel to the y-axis experiencesrefractive index n_(o) whatever the tilt angle θ is, and therefore thephase delay caused to it by the cell is independent of the voltageacross it (ordinary wave). On the contrary, the length of the major axisdoes depend on the tilt angle θ, and so the x-component of the field(extraordinary wave) experiences different refractive index n fordifferent values of the tilt angle.

The length of the major axis 111 is n(θ), and is given by equation (1):$\begin{matrix}{\frac{1}{n^{2}(\theta)} = {\frac{\cos^{2}(\theta)}{n_{o}^{2}} + \frac{\sin^{2}(\theta)}{n_{e}^{2}}}} & (1)\end{matrix}$

It follows that n₀≦n(θ)≦n_(e). The relative phase delay between the twocomponents is then given by the equation (2):Δφ=k ₀ dΔn  (2)

In equation (2), d is the thickness of the liquid crystal cell, k₀ thewavenumber of the field in free space and Δn is given by Δn=n(θ)−n_(o).Since Δn is a function of the voltage across the cell, equation (2)shows that the applied voltage can continuously control the phasedifference between the two components across the cell.

It will be understood by those skilled in the art that it is desirableto provide phase modulation that is not sensitive to polarisation, anddevices and methods for achieving this will now be described for thesituation of normally incident light:

Expression (3) shows a mathematical representation of an arbitrarypolarisation state as the superposition of two orthogonal, linearlypolarised waves: $\begin{matrix}{{E_{IN}\left( {x,y,z,t} \right)} = {\begin{pmatrix}{{E_{0X}(t)}\exp\quad{{jɛ}_{x}(t)}} \\{{E_{0Y}(t)}\exp\quad{{jɛ}_{Y}(t)}}\end{pmatrix}\exp\quad{j\left( {{kz} - {\omega\quad t}} \right)}}} & (3)\end{matrix}$where the amplitudes, E_(0Y)(t) and E_(0X)(t), and phases ε_(X)(t) andε_(Y)(t) vary slowly, remaining essentially constant over a large numberof oscillations. For unpolarised light the relative amplitude,E_(0Y)(t)/E_(0X)(t) and relative phase, ε_(Y)(t)−ε_(X)(t), vary rapidlycompared to the coherence time of each linearly polarised component,i.e. the two waves are mutually incoherent. For randomly polarised lightthe relative amplitude and phases vary slowly with respect to thecoherence time, i.e. the two waves are mutually coherent. Hence theabove representation is valid for any light wave.

Such light could be modulated by applying the same phase delay to bothof these components. However, the configuration in FIG. 2, allows justone of the two components (x-component) to be properly phase-modulatedsince the y-component always gains the same phase delay.

FIG. 3 shows a schematic diagram of a configuration that would allow forboth components to be modulated. Referring to FIG. 3, light is reflectedfrom a mirror 30 after passing through a liquid crystal cell 32 toenable a double-pass configuration. In between the two passes a suitablerotator 31 is introduced, which rotates both components through 90°. Asis known to those skilled in the art, a quarter-wave plate acts toretard one polarisation component of light relative to the orthogonallypolarised component; thus the combination of a quarter-wave plate (withan optical axis tilted out of the plane Oxz by 45°) and a mirror acts asa 90° rotator. It would of course be possible to use a ¾, 5/4 etc-waveplate, the criterion being an odd-integer number of quarter waves, sothat a double pass produces the overall 90° rotation. Consider lightwith an arbitrary polarisation state (as in expression 3) at normalincidence passing through the configuration shown in FIG. 3. Differencesfor off-normal incidence will be considered later.

For the first pass, on the way towards the quarter wave plate andmirror, the polarisation component polarised in the xdirection(E_(0X)(t) exp j ε_(X)(t)) experiences a refractive index n(θ), where θdepends on the applied voltage, while the component in the y direction(E_(0Y)(t) exp j ε_(Y)(t)) does not, and instead experiences arefractive index, n₀, that is independent of the applied voltage. Theorientation of the quarter wave plate is such that these twopolarisation components are exchanged. For the 2^(nd) pass, on returningback through the liquid crystal, the component E_(0X)(t) exp j ε_(X)(t))is now polarised in the y direction, and therefore experiences arefractive index n₀, while the component E_(0Y)(t) exp j ε_(Y)(t) is nowpolarised in the x direction, and experiences a refractive index n(θ).In this way both components gain overall the same amount of phase delaythrough the system since they both experience one pass under arefractive index n(θ) and one pass under a refractive index n_(O).

In particular (equations 4 and 5):E _(OX) component: Δφ_(OX)=Δφ_(1ST-PASS)+Δφ_(2ND-PASS) =kn(θ)d+kn ₀d  (4)E _(OY) component: Δφ_(OY)=Δφ_(1ST-PASS)+Δφ_(2ND-PASS) =kn ₀d+kn(θ)d  (5)

The system may be described mathematically (equation 6) in terms ofJones matrices, with the result that (as expected): $\begin{matrix}\begin{matrix}{{E_{OUT}\left( {x,y,z,t} \right)} = \begin{pmatrix}0 & {\exp\quad{{jkd}\left( {n_{0} + {n(\theta)}} \right)}} \\{\exp\quad{{jkd}\left( {n_{0} + {n(\theta)}} \right)}} & 0\end{pmatrix}} \\{\begin{pmatrix}{{E_{0X}(t)}\exp\quad{{jɛ}_{x}(t)}} \\{{E_{0Y}(t)}\exp\quad{{jɛ}_{Y}(t)}}\end{pmatrix}\exp\quad{j\left( {{kz} - {\omega\quad t}} \right)}} \\{= \begin{pmatrix}{{E_{0Y}(t)}\exp\quad j\left\{ {{ɛ_{Y}(t)} + {{kd}\left( {n_{0} + {n(\theta)}} \right)}} \right\}} \\{{E_{0X}(t)}\exp\quad j\left\{ {{ɛ_{x}(t)} + {{kd}\left( {n_{0} + {n(\theta)}} \right)}} \right\}}\end{pmatrix}} \\{\exp\quad{j\left( {{kz} - {\omega\quad t}} \right)}}\end{matrix} & (6)\end{matrix}$

It should however be noted that the light exits the system in theopposite orthogonal state. This Jones matrix result uses the conventionthat the y-axis is inverted on reflection from the mirror. Themathematical result confirms that both components of the output lighthave the same phase change (in agreement with equation 4 and 5) andtherefore polarisation insensitive phase modulation is feasible.

In general θ may vary with z, in which case the index n(θ) in (6) shouldbe replaced by (expression 7): $\begin{matrix}{{n(\theta)}->{\frac{1}{d}{\int_{z = 0}^{d}{{n\left( {\theta(z)} \right)}\quad{\mathbb{d}z}}}}} & (7)\end{matrix}$

The foregoing principle can be applied to an array of modulatingelements. A plane wave front of arbitrarily polarised light, whichnormally impinges on to such an array of pixels, each of which ischaracterised by a specific value of tilt angle (by the application ofdifferent voltages across it), or a specific distribution of tiltangles, can be spatially phase modulated.

Referring now to FIG. 4, a first embodiment of an integrated spatiallight modulator in accordance with the invention will now be described:

AS seen in FIG. 4, the SLM consists of an aluminium pad 120, which formsa pixel array, and is connected to pixel driving circuitry by aconnection figuratively shown at 126. On the pixel array 120 there isdisposed a quarter-wave plate 121. On the quarter-wave plate, and overan intervening alignment layer, (not shown) there is disposed a liquidcrystal layer 122—here a nematic liquid crystal is used, but theinvention is not so limited. The actual requirement is the ability toprovide an out of plane tilt. On the liquid crystal layer there is analignment layer 123, as known to those skilled in the art, and over thealignment layer there is disposed a transparent conductive layer 124such as an ITO (Indium Tin Oxide) layer forming a common electrodeplane, and an upper glass layer 125.

The quarter-wave plate can be deposited on the pixel array byspin-coating a proper reactive monomer, which can be polymerised byexposure to ultraviolet light. In the cell of FIG. 4, the aluminium padacts as a mirror and also provides the necessary power voltage acrossthe cell for the liquid crystal 122 to switch.

A second embodiment is shown in FIG. 5.

Referring to FIG. 5, a pixel array 130 is integrated on a silicon-1.5μm-transparent backplane structure 131, and is sandwiched between thebackplane structure and one face of a liquid crystal layer 132. Theother side of the liquid crystal layer 132 is in contact with analignment layer 133, which in turn is covered by an ITO layer 134. Aquarter wave-plate 135 is disposed between a front aluminium mirror 136and the ITO electrode 134. The thickness of the quarter wave plate maybe adjusted by spin-coating techniques so that in reflection itfunctions as a half-wave plate at λ=1.57 μm.

An embodiment of a spatial light modulator in accordance with FIG. 5 wasconstructed. The pixels were constructed using the polysilicon layer ofa conventional 2 μm CMOS process. FIG. 6 shows an overview of thesilicon backplane layout.

Referring to FIG. 7 a further embodiment of the invention uses a twistednematic liquid crystal mixture in a π-cell configuration, again using aquarter-wave plate. Such a device enables reduced liquid crystalresponse time. In such cells the director of the nematic liquid crystaltwists along the thickness of the cell through an angle. FIG. 7A showsthe director angle as a series of illustrative lines 50-56 across thecell thickness, with the cell in the unbiased state. FIGS. &B shows theother extreme condition with maximum bias, with the directors forming astraight line between the front and rear plates. In a pi cell flow ofmaterial within the cell during the switching process is minimised andthe response time decreases. Given that the thickness of the cell islarge enough so that the field can be actually wave-guided through it,the same principle of FIG. 2 applies and the cell can give fast,polarisation insensitive switching.

Although the above discussions are in the context of an integralretarder, it is also possible to use a non-integral retarder, such as anon-integral quarter wave plate. The following description is nottherefore limited to an integral quarter wave plate.

Referring now to FIG. 8, a first partial diagram of an embodiment of areflective switch uses a first, or input SLM 140 and a second, or outputSLM 141, each divided into a set of blocks (or holograms), and disposedspaced apart and generally parallel to and on opposite sides of an axisof symmetry 142. The two SLMs face the axis 142, and are spaced alongit. An input fibre array 143 having an input fibre FC is directedtowards the first SLM 140, and is disposed such that light from thefibres in the array are incident upon the input SLM at an angle θ_(in)to a plane normal to the plane of the SLM. An output fibre array 144having an output fibre fB is similarly directed with respect to theoutput SLM 141. Thus light describes a generally zigzag path from theinput fibres of the input array, to the first SLM 140, then to thesecond opposing output SLM 141 and finally to a fibre of the outputarray 144. As discussed above, each SLM displays plural holograms, andthe disposition of the system is such that for the input SLM 140, eachhologram is associated with a particular input fibre, while for theoutput SLM 141, each hologram is associated with a particular outputfibre.

Routing from input fibre fC to output fibre fB is achieved byconfiguring input hologram hC to deflect the input beam to outputhologram hB, so that the angle of reflection typically differs from theincident angle θ_(in). Output hologram hB deflects the beam incident onit to output fibre fB. In between each hologram and its correspondingfibre there is an optical system, embodiments of which are describedlater herein, that has the function of presenting beams of appropriatediameter to the hologram.

In order to minimise the system losses, it is desirable to have as fewlenses as possible in the optical system. A first optical system, foruse with the switch of FIG. 9, is shown in FIG. 9. Referring to FIG. 9,the optical system has a first 150 and a second 151 confocal lens in atelescopic arrangement. The system has the fibre array 143 to the left,as shown, of the first lens 150, and the SLM 140 on the right of thesecond lens 151. The focal length f₁ of the first lens 150 is shorterthan the focal length f₂ of the second lens 151. The fibre array 143 ispositioned at the input focal plane of the first lens 150, while theoutput focal plane of the second lens 151 is approximately midwaybetween the hologram devices 140, 141 (see FIG. 8). The same systemwould be used at both input and output to the switch. Under certaincircumstances, as will be clear to those skilled in art, a fieldflattening lens may be required.

In a co pending patent application an embodiment using reflective SLMshas the beam passing twice through a lens (off-axis) positionedimmediately in front of the SLM.

The system of FIG. 9 has a relatively low wavelength range. However, anumber of measures can be used to improve the wavelength range. Theseinclude:

-   -   use of fibres with a larger spot-size, such as TEC (Thermally        Expanded Core) fibres:    -   use of fibres with a narrower diameter thus allowing closer        packing; and    -   use of a microlens array after the fibre array, so that the        focused spots leaving the microlens array are in the input focal        plane of the lens of lower focal length (see FIG. 10 in which a        microlens array 153 having focal length f_(m) is between the        lens 150 and the input fibre array 143. The input microlens        array 153 is disposed with respect to the input fibres so as to        focus light from those fibres to the focal plane of the lens        150).

An advantageous option is to use both a microlens array and largerspot-size fibres in the fibre array.

As will be clear to those skilled in the art, the required number ofpixels in each row of the hologram, M, may be calculated using the beamspot size of the hologram and the maximum beam steering angle, and thecross talk requirement.

The requirements of optimum performance suggest the use of eitherstandard fibres with a microlens array or fibres with larger thanstandard spot size.

As known to those skilled in the art, a quarter-wave plate will onlywork perfectly for one particular wavelength, giving rise to errors atother wavelengths. Deviations from the theoretical also result fromfabrication tolerances in the quarter-wave plate thickness andbirefringence, and from misalignments between the plate orientation andthe plane of tilt of the liquid crystal.

It can be shown that these effects produce zero-order (i.e.undiffracted) polarisation-dependent crosstalk in a switch configurationdue to the component of incident light in the y polarisation direction.

For incident light polarised in the x direction, it can be shown thatthe result of the errors is to produce a diffraction order at twice theangle of the intended main diffraction order. The amplitude of thisdoubled-order crosstalk varies with the polarisation state of the inputlight, and hence the effect is to generate polarisation-dependentcrosstalk.

Reference to FIG. 8 shows that the input and output holograms deflectthe beam in opposite directions. As known, maximal wavelength range isachieved when angular deflection is equal and opposite. The consequenceis that, with the SLMs parallel as shown, the beams travelling from theinput fibres to the input holograms are parallel to the beams travellingfrom the output holograms to the output fibres.

As the hologram array is regular, such that the set of tilt angles isquantised into units of Mp/L, where M is the number of pixels in eachrow of the hologram, p is the pixel pitch, and L is the distance betweenthe holograms, therefore to route to a fibre n_(X) along in the xdirection, and n_(y) along in the y direction, the beam deflection atthe input hologram is given by equation 8: $\begin{matrix}{{\delta\left( {\sin\quad\theta_{X}} \right)} = {{\frac{n_{X}{Mp}}{L}\quad{and}\quad{\delta\left( {\sin\quad\theta_{Y}} \right)}} = \frac{n_{Y}{Mp}}{L}}} & (8)\end{matrix}$

Also the beam deflection at the output hologram is (equation 9):$\begin{matrix}{{\delta\left( {\sin\quad\theta_{X}} \right)} = {{{- \frac{n_{X}{Mp}}{L}}\quad{and}\quad{\delta\left( {\sin\quad\theta_{Y}} \right)}} = {- \frac{n_{Y}{Mp}}{L}}}} & (9)\end{matrix}$

Referring now to FIG. 11, the output SLM 141 is arranged such that thezero-order beam reflected from the centre of any hologram on the inputSLM 140 is incident on the centre of an output hologram of the outputSLM 141. This is the configuration that maximises the wavelength range.For example, the zero-order reflection from hologram hA is incident onthe centre of hologram hB.

The effect of the quarter-wave plate tolerances is to route a beam 145of amplitude a_(yy) from hologram hA on input SLM 140 to hologram hB onoutput SLM 141, where a_(YY) is the fraction of incident light polarisedin the y direction which remains in that state after transition throughthe first SLM 140. Analogous effects at the second SLM 141 cause a beam146 of net amplitude of up to (a_(YY))² to pass into the zero-orderoutput from hologram hB. As a result of the system geometry, thezero-order beam 146 reaches output fibre fC. Hence the effect of the ypolarised light that remains in this polarisation state is to causecrosstalk in fibre fC of maximum amplitude (a_(YY))² from the signalentering the switch at fibre fA. The remainder of the light fromhologram hA directed to hologram hB has amplitude a_(YY)(1−a_(YY)). Thislight will be subject to the intended deflection angle introduced byhologram hB, and will form a light beam 147. Let the distance inhologram units between holograms hA and hC on first, input SLM 140 be(d_(X),d_(Y)). What happens next depends on the design of the system.For the basic system (microlens-free system), the beam will enter outputfibre fC at a tilt angle. The system may be designed such that thislight (of maximum amplitude a_(YY)(1×a_(YY))) is partially attenuated bythe limited angular acceptance of the output fibre (or offsetacceptance, depending on the optical architecture). It may be shown thatthe attenuation, α_(TILT), due to this tilt is given by equation 10:$\begin{matrix}{{\alpha_{TILT} = {\left( {d_{X}^{2} + d_{Y}^{2}} \right)\alpha_{T}\quad{where}}}{\alpha_{T} = {- \frac{5C^{2}\log_{10}e}{1 - \left( {C\quad{\omega/s}} \right)^{2}}}}} & (10)\end{matrix}$where C is the clipping parameter at the hologram, such thatMp=C.ω_(HOL), where ω_(HOL) is the beam spot-size at the hologram. Witha switch configured for maximum wavelength range, the worst-case valueof d_(X) ²+d_(Y) ² is unity. To improve crosstalk suppression, α_(TILT)should be as high as possible: thus performance is improved byincreasing the value of the ratio of the spot-size to the fibreseparation.

Referring to FIG. 12, a second embodiment of an optical switch differsfrom that shown in FIG. 8 by disposing a half-wave plate 150 between thetwo spatial light modulators 140, 141. The half=wave plate exchanges fora second time the x and y polarisation components so that the residualzero order beam 151(of maximum amplitude a_(YY)) from the first SLM 140is x polarised on reaching the second SLM 141. of this light a firstoutput beam 152 results from a fraction a_(XX) being deflected by twicethe intended deflection angle, and there is thus no longer crosstalkdirected precisely at output fibre fC. In fact this beam is deflected soit comes in at twice the tilt (or twice the offset, depending on thearchitecture), and the attenuation is scaled up by a factor of 4. Therest of this polarisation-dependent zero-order light is again deflectedby the intended deflection angle, and is subject to the same attenuationas for the system without a central half-wave plate.

Referring to FIG. 13, a third embodiment of an optical switch accordingto the invention has the second SLM 141 offset by half a hologram'swidth in one plane (e.g. the x direction) . Thus zero-order crosstalk145, including the polarisation-dependent zero order, is directed at apoint midway 149 between output fibres. In this case the zero-ordercrosstalk is subject to an offset of s/2, with a correspondingadditional attenuation dependent on the offset.

The third embodiment is most appropriate in the presence of good surfaceflatness on the SLM. For the case of offset loss, it reduces as theratio of the spot-size to the fibre separation is increased. In anyfinal design there will be an optimum value of this ratio to obtain theoverall required system performance.

Referring now to FIG. 14, in a further embodiment a further reduction ofthe zero order is achieved by offsetting the output SLM 141 with respectto the input SLM 140 by a whole SLM's height (or more) in the directionnormal to the plane of incidence. The figure shows two light beams 70 a,70 b, each incident on a first SLM 140, and having a zero-orderreflection from that SLM to define a respective plane of incidence. Itcan be seen that each plane of incidence is horizontal—the x-z plane.The output SLM 141 is offset downwardly so that zero orders do notimpinge on it. Alternatively, an upward shift could be employed. Thisembodiment offers resilience to the effects of bowing or long-rangesurface distortion of the reflective surface inside the SLM. In thiscase the zero orders fall outside of the output fibre array, and can beconveniently used for monitoring purposes, for example.

Now consider the polarisation-dependent doubled orders, in a 2-D system.Let these be approaching the output hologram at deflection angles(equation 11): $\begin{matrix}{{\delta\left( {\sin\quad\theta_{X}} \right)} = {{\frac{c_{X}{Mp}}{L}\quad{and}\quad{\delta\left( {\sin\quad\theta_{Y}} \right)}} = \frac{c_{Y}{Mp}}{L}}} & (11)\end{matrix}$

In the zero-order aligned system (FIG. 8) the possible values of c_(X)and c_(Y) are always even, while n_(X) and n_(Y) can take any integervalues. Hence it is possible for doubled orders from the input SLM 140to arrive at the centres of output holograms, and afterwards be focuseddirectly, or at a tilt, into an output fibre. In the zero-orderinterleaved system (FIG. 10), however, the possible values of c_(X) arealways odd integers, while n_(X) can only take half-integer values.Hence the doubled orders from the input SLM 140 will arrive between theoutput holograms, and will be focused directly, or at a tilt, intopoints midway between output fibres. Hence zero-order interleaving alsocreates doubled-order interleaving.

In a preferred embodiment, the attenuation of beams arriving between theoutput fibres is increased by adding black paint to the glue holding thefibres together inside the fibre array. It will be understood that otherabsorbers could also be used. In another embodiment, the spacing betweenthe fibres of the array is occupied by interstitial fibres which serveto accept and guide away cross talk from the switching zone. Theamplitude of the doubled-order beam is at most a_(XX). In the absence ofa central half-wave plate, there will be a beam of maximum amplitudea_(XX) ² coming out at deflection angles (with reference to beamsfocused directly into an output fibre) given by equation 12:$\begin{matrix}{{\delta\left( {\sin\quad\theta_{X}} \right)} = {{\frac{\left( {c_{X} - {2n_{X}}} \right){Mp}}{L}\quad{and}\quad{\delta\left( {\sin\quad\theta_{Y}} \right)}} = \frac{\left( {c_{Y} - {2n_{Y}}} \right){Mp}}{L}}} & (12)\end{matrix}$

The worst-case scenario is that c_(X)=2n_(X), and c_(Y)=2n_(Y). In thiscase for the zero-order aligned system (FIG. 11), the beam of maximumamplitude a_(XX) ² will be focused directly down the output fibre. Whilefor the zero-order interleaved system (FIG. 13), this beam will befocused in between the output fibres, and will therefore be subject toan offset loss.

In the presence of a central half-wave plate, a weak beam, of maximumamplitude a_(XX)a_(YY), will be reflected as a zero-order reflection,and will therefore come out at deflection angles given by equation 13:$\begin{matrix}{{\delta\left( {\sin\quad\theta_{X}} \right)} = {{\frac{c_{X}{Mp}}{L}\quad{and}\quad{\delta\left( {\sin\quad\theta_{Y}} \right)}} = \frac{c_{Y}{Mp}}{L}}} & (13)\end{matrix}$

Firstly consider what happens in the zero-order aligned system (FIG.11): this beam is attenuated at the output fibre due to the limitedangular acceptance. Either c_(X) or c_(y) could be zero, in which casethe minimum value of the tilt loss at the output fibre is 4α_(T).

Now consider what happens in the zero-order interleaved system (FIG.13). The worst-case is c_(Y)=0 and c_(X)=1: the beam will be attenuatedby a tilt loss of α_(T) and also the above described offset loss. Inaddition, if the output SLM is offset vertically, then the minimum valueof n_(Y) is 1, in which case the beam will additionally be attenuated bya tilt loss of 4 α_(T).

Now consider the remaining light in the incident doubled order. Withouta central half-wave plate, this beam will have a maximum amplitude ofa_(XX)(1−a_(XX)), while in the presence of a central half-wave plate,this beam will have a maximum amplitude of a_(XX)(1−a_(YY)). With orwithout the central half-wave plate, this beam is deflected by theintended deflection angle, and so leaves the output hologram at adeflection angle given by equation 14: $\begin{matrix}{{\delta\left( {\sin\quad\theta_{X}} \right)} = {{\frac{\left( {c_{X} - n_{X}} \right){Mp}}{L}\quad{and}\quad{\delta\left( {\sin\quad\theta_{Y}} \right)}} = \frac{\left( {c_{Y} - n_{Y}} \right){Mp}}{L}}} & (14)\end{matrix}$

For the zero-order aligned system, the worst-case is for eitherc_(X)=n_(X) or c_(Y)=n_(Y), but not both. Assume that one of these istrue. The minimum attenuation is when |c_(X)−n_(X)|=1 or when|c_(Y)−n_(Y)=1 and so the beam will be attenuated by a tilt loss ofα_(T). For the zero-order interleaved system, the minimum attenuation iswhen |c_(X)−n_(X)=½ and |c_(Y)−n_(Y)|=0. The minimum, attenuation isthen 0.25α_(T), added to the offset loss. If additionally, the outputSLM 141 is offset by an odd integer number of hologram heights, then theoffset loss is doubled from that previously defined, and the minimumvalue of |c_(Y)−n_(Y)| becomes ½, so the tilt attenuation is increasedto 0.5 α_(T).

To maintain desired back reflection conditions off-normal incidence ispreferable: it is likely to occur in any event due to the geometricalconstraints of the system. However the closer to normal incidence, thebetter is the performance.

Where the beam has off-normal incidence, the phase of the reflectioncoefficient from the mirror of the SLM becomes polarisation-dependent,due to plasmon resonances in the metal mirror. The effect is to increasethe fraction of light in each polarisation state that remains in thatstate after passing back through the quarter-wave plate. Another effectof off-normal incidence through the quarter-wave plate is to change, forthe worse, both the effective thickness and also the birefringence.Hence a consequence of off-normal incidence is to increase the strengthof the polarisation-dependent crosstalk into the zero and doubledorders.

Given off-normal incidence, it now becomes necessary to choose the planeof incidence. In this section the effects of off-normal incidence, butstill in the x-z plane, are investigated.

Assume the Poynting vector of the incident light to be in the xOz plane,with a polarisation component E_(OY)(t) exp j ε_(Y)(t) in the ydirection, and E_(0XZ)(t) exp j ε_(xZ)(t) in the xOz plane (in adirection mutually orthogonal to y and the Poynting vector).

Let the light be incident at an angle θ_(INC) to the mirror, as shown inFIG. 15, and let the long axis of the index ellipsoid be in the xOzplane, at an angle θ_(D) to the x-axis. A geometric method as discussedpreviously may be used to analyse the propagation. As before, the indexellipse is defined by the intersection of the plane perpendicular to thePoynting vector with the index ellipsoid. As long as the Poynting vectorremains in the xOz plane, the light component polarised in the ydirection and travelling towards the mirror (E_(0Y)(t) exp j ε_(Y)(t))experiences a refractive index n₀, that is independent of the tiltangle. This means that even if the tilt angle is changing in the zdirection, the y polarised component still perceives a constantrefractive index. This index is also independent of the angle ofincidence. The index experienced by the orthogonal component (E_(0XZ)(t)exp j ε_(xZ)(t)) is the length of the major axis of this ellipse. Onpropagation towards the mirror the major axis is at an angleθ_(D)−θ_(INC) to the director in the xOz plane: the length and directionof this axis is shown by the line AB on the figure. Mathematically theindex experienced by the orthogonal component (E_(0XZ)(t) exp jε_(xZ)(t)) is given by substituting θ=θ_(D)−θ_(INC) into equation (1).After reflection from the mirror and passing back through the quarterwave plate it is the component E_(0Y)(t) exp j ε_(Y)(t) that ispolarised in the xOz plane. For this second pass, the major axis of theindex ellipse is now at an angle θ_(D)+θ_(INC) to the director in thexOz plane: the length and direction of this axis is shown by the line ACon the figure. Mathematically the index experienced by the orthogonalcomponent (E_(0XZ)(t) exp j ε_(xZ)(t)) is given by substitutingθ=θ_(D)+θ_(INC) into equation (1). Hence the phase delays for the twocomponents are now given by equations 15 and 16:

E_(0XZ) component:Δφ_(OXZ)=Δφ_(1ST-PASS)+Δφ_(2ND-PASS) =kn(θ_(D)−θ_(INC))d+kn ₀ d  (15)

E_(OY) component:Δφ_(OY)=Δφ_(1ST-PASS)+Δφ_(2ND-PASS) =kn ₀ d+kn(θ_(D)+θ_(INC))d  (16)

Therefore the phase-modulation now has a weak polarisation dependence,which increases with the angle of incidence, and is given approximately(to second order) by equation 17: $\begin{matrix}{{{\Delta\phi}_{0Y} - {\Delta\phi}_{0{XZ}}} = {{2k\quad\theta_{INC}\frac{\partial n}{\partial\theta}}❘_{\theta_{D}}}} & (17)\end{matrix}$

In a cell in which the tilt angle is varying (as in 7), the polarisationdependence of the phase modulation is given by equation 18:$\begin{matrix}{{{\Delta\phi}_{0Y} - {\Delta\phi}_{0{XZ}}} = {{\frac{2k\quad\theta_{INC}}{d}{\int_{z = 0}^{d}\frac{\partial{n\left( {\theta(z)} \right)}}{\partial\theta}}}❘_{\theta}\quad{\mathbb{d}z}}} & (18)\end{matrix}$

The rate of change of n with respect to director angle is easily shownto be (equation 19): $\begin{matrix}{\frac{\partial n}{\partial\theta} = {\frac{n^{3}(\theta)}{2}\sin\quad 2{\theta\left( {\frac{1}{n_{0}^{2}} - \frac{1}{n_{e}^{2}}} \right)}}} & (19)\end{matrix}$

Note that for tilt angles in the range 0 to π/2, this derivative isalways negative, while for tilt angles in the range π/2 to π, thederivative is always positive. For a pi cell, the tilt angle θ variesbetween 0 and π. Hence the polarisation-dependent phase modulations maypartially cancel.

An important property of this plane of incidence, is that of thedirections of the two polarisation modes. Bearing in mind that these aregiven by the directions of the minor and major axes of the ellipseformed by the intersection of the plane perpendicular to the Poyntingvector, with the index ellipsoid, if the Poynting vector is in the xOzplane, then the minor axis is always in the y direction and the majoraxis is always in the xOz plane (and parallel of course to the xOzcomponent of the incident light). Therefore the polarisation states ofthe y polarised and orthogonal components of the incident light are notchanged inside the liquid crystal, and therefore proper polarisationcomponent exchange should still take place at the quarter-wave plate andmirror. Returning now to the polarisation-dependence, the effect on abeam-steering device, is to introduce a polarisation-dependence into theamplitude (but not the output angle) of each diffraction order, wherethis polarisation-dependence is a function of the angle of incidence.Now consider an NxN switch using two such devices, and let the SLM shownin FIG. 15 be the input SLM. In order to keep the mathematics simple, ananalysis is now presented for 1-D SLMs, and hence 1-dimensionalbeam-steering. The results of this analysis hold good for twodimensional SLMs. Define Fourier coefficients a_(L1) and b_(L1) suchthat (equations 20 & 21): $\begin{matrix}{a_{L1} = {{\int_{u = {- \infty}}^{\infty}{\exp\quad{\mathbb{i}}\left\{ {{{{kn}_{o}d} + {\phi(u)} - {{kd}\quad\theta_{INC}\frac{\partial n}{\partial\theta_{D}}}}❘_{\theta_{D}{(u)}}} \right\}\exp}} - {{{\mathbb{i}}\left( \frac{{2\pi\quad{Lu}}\quad}{\Omega} \right)}{\mathbb{d}u}}}} & (20) \\{b_{L1} = {{\int_{u = {- \infty}}^{\infty}{\exp\quad{\mathbb{i}}\left\{ {{{{kn}_{o}d} + {\phi(u)} + {{kd}\quad\theta_{INC}\frac{\partial n}{\partial\theta_{D}}}}❘_{\theta_{D}{(u)}}} \right\}\exp}} - {{{\mathbb{i}}\left( \frac{2\pi\quad{Lu}}{\Omega} \right)}\quad{\mathbb{d}u}}}} & (21)\end{matrix}$where u is the position co-ordinate of each pixel, and φ(u) is theintended phase modulation, as defined immediately before equation (13).Hence for the input SLM, the y polarised component of the incident fieldis diffracted into orders of amplitude b_(L1), while the orthogonalcomponent is diffracted into orders of amplitude a_(L1). For awell-designed hologram, almost all of the power will go into a singlediffraction order.

It is assumed that the input and output SLMs are made in the same way.Now consider pixels in the two SLMs applying the same nominal phasemodulation (for a normally incident beam), and hence having the sametilt angle, θ_(D). Due to the geometry of the arrangement of SLMs etc,the beam entering the 1st SLM is parallel to the beam leaving the secondSLM, as shown in FIG. 16. Let there again be a half-wave plate betweenthe two SLMs.

The y polarised component of the field incident on the 1st SLM, ispolarised in the xOz plane on leaving the 1st SLM, and due to thehalf-wave plate is again y polarised on entering the second SLM. Thiscomponent perceives the ordinary index n₀ on propagation towards themirror. On propagation away from the mirror, the index perceived isgiven by an effective tilt angle of θ=θ_(D)−θ_(INC). Hence the totalphase delay for this component is given by (equation 22):

E_(OY) component:Δφ_(OY)=Δφ_(1ST-PASS)+Δφ_(2ND-PASS) =kn(θ_(D)−θ_(INC))d+kn ₀ d  (22)

Similarly, it can be shown that for the orthogonal polarised component(in the xOz) plane of the beam incident on the 1st SLM, the phasemodulation at the second SLM is given by (equation 23):

E_(OXZ) component:Δφ_(OXZ)=Δφ_(1ST-PASS)+Δφ_(2ND-PASS) =kn ₀ d+kn(θ_(D)+θ_(INC))d  (23)

At the second SLM, and assuming substantially flat SLMs, the hologram issubstantially complementary to that at the first SLM. Let the intendedphase modulation at the second SLM be φ_(c)(u), and let the directorangle be θ_(c)(u). If at the input SLM, the hologram is designed tomaximise the output into the L′th diffraction order, then at the outputSLM, the hologram should maximise the output into the −L′th diffractionorder. For this output SLM therefore, the Fourier coefficient b_(−L2)that defines the amplitude of the main diffraction order for the ypolarised component of the field incident on the 1st SLM is given by(equation 24): $\begin{matrix}{b_{- {L2}} = {{\int_{u = {- \infty}}^{\infty}{\exp\quad{\mathbb{i}}\left\{ {{{{kn}_{o}d} + {\phi_{C}(u)} - {{kd}\quad\theta_{INC}\frac{\partial n}{\partial\theta_{C}}}}❘_{\theta_{C}{(u)}}} \right\}\exp}} + {{{\mathbb{i}}\left( \frac{2\pi\quad{Lu}}{\Omega} \right)}\quad{\mathbb{d}u}}}} & (24)\end{matrix}$while the Fourier coefficient for the main diffraction order from theoutput SLM for the orthogonal component of the field incident on the 1stSLM is given by (equation 25): $\begin{matrix}{a_{- {L2}} = {{\int_{u = {- \infty}}^{\infty}{\exp\quad{\mathbb{i}}\left\{ {{{{kn}_{o}d} + {\phi_{C}(u)} + {{kd}\quad\theta_{INC}\frac{\partial n}{\partial\theta_{C}}}}❘_{\theta_{C}{(u)}}} \right\}\exp}} + {{{\mathbb{i}}\left( \frac{{2\pi\quad{Lu}}\quad}{\Omega} \right)}{\mathbb{d}u}}}} & (25)\end{matrix}$

The overall holographic switching efficiency for the y polarisedcomponent of the field incident on the 1st SLM is given by (equation26):η_(0Y) =|b _(L1)|² |b _(−L2)|²  (26)while the overall holographic switching efficiency for the orthogonalcomponent of the field incident on the 1st SLM is given by (equation27):η_(OXZ) =|a _(L1)|² |a _(−L2)|²  (27)

Now consider the hologram patterns, and let the local director angle,θ_(D)(u) be expressed in terms of some fundamental repeating pattern,θ₁(u) (equation 28): $\begin{matrix}{{\theta_{D}(u)} = {{\theta_{1}(u)}*{\sum\limits_{J = {- \infty}}^{\infty}{\delta\left( {{J\quad\Omega} - u_{0}} \right)}}}} & (28)\end{matrix}$

Given that the intended or mean phase modulation on the 1st SLM, φ(u),depends on the local director angle (equations 1 and 7), then it mustalso show periodicity with the same period Ω, as must any derivativeswith respect to θ_(D)(u) (equation 19). Therefore, taking into accountthe effects of off-normal incidence as in equations 20,21 etc, the netphase modulation will still be periodic with the same period. Hence wemay define H⁻(u) such that (equation 29) $\begin{matrix}{{\exp\quad{\mathbb{i}}\left\{ {{{{kn}_{o}d} + {\phi(u)} - {{kd}\quad\theta_{INC}\frac{\partial n}{\partial\theta_{D}}}}❘_{\theta_{D}{(u)}}} \right\}} = {{H^{-}(u)}*{\sum\limits_{J = {- \infty}}^{\infty}{\delta\left( {{J\quad\Omega} - u_{0}} \right)}}}} & (29)\end{matrix}$where u₀ is some (arbitrary) origin. This origin affects the phase, butnot the magnitude, of the diffraction orders. The magnitude of a_(L1)may be obtained in terms of H(u) using Fourier series analysis (equation30): $\begin{matrix}{{a_{L1}} = {\frac{2}{\Omega}{{{\int_{{- \Omega}/2}^{\Omega/2}{{H^{-}(u)}\exp}} - {{\mathbb{i}}\quad\frac{{2\pi\quad{Lu}}\quad}{\Omega}{\mathbb{d}u}}}}}} & (30)\end{matrix}$

Similarly, let θ_(c)(u) be the director angle on the 2nd hologram, andexpress it in terms of another fundamental repeating pattern, θ₂(u)(equation 31): $\begin{matrix}{{\theta_{C}(u)} = {{\theta_{2}(u)}*{\sum\limits_{J = {- \infty}}^{\infty}{\delta\left( {{J\quad\Omega} - u_{1}} \right)}}}} & (31)\end{matrix}$

Therefore, using the same arguments as above, the phase modulation onthe second SLM must also be periodic with period Ω, and so we may defineG⁻(u) such that (equation 32): $\begin{matrix}{{\exp\quad i\left\{ {{{{kn}_{o}d} + {\phi_{C}(u)} - {{kd}\quad\theta_{INC}\frac{\partial n}{\partial\theta_{C}}}}❘_{\theta_{c}{(u)}}} \right\}} = {{G^{-}(u)}*{\sum\limits_{J = {- \infty}}^{\infty}{\delta\left( {{J\quad\Omega} - u_{1}} \right)}}}} & (32)\end{matrix}$where u₁ is another arbitrary origin. Hence we may calculate themagnitude of b_(−L2) (equation 33): $\begin{matrix}{{b_{- {L2}}} = {\frac{2}{\Omega}{{{\int_{{- \Omega}/2}^{\Omega/2}{{G^{-}(u)}\exp}} + {{\mathbb{i}}\quad\frac{2\pi\quad{Lu}}{\Omega}\quad{\mathbb{d}u}}}}}} & (33)\end{matrix}$

If we let G⁻(u)=H⁻(−u), and make the substitution u′=−u, it is clearthat (equation 34):|a _(L1) |=|b _(−L2)|  (34)

Physically this may be achieved by making the repeating pattern θ₂(u) onthe second SLM equal to θ₁(−u) on the first SLM. In which case (fromequation(1)), φ_(c)(u)=φ(−u) as required. Now consider the other twoamplitude coefficients. At the first SLM, define a periodic phasemodulation H⁺(u), and use the same origin (equation 35): $\begin{matrix}{{\exp\quad i\left\{ {{{{kn}_{o}d} + {\phi(u)} + {{kd}\quad\theta_{INC}\frac{\partial}{\partial\theta_{D}}}}❘_{\theta_{D}{(u)}}} \right\}} = {{H^{+}(u)}*{\sum\limits_{J = {- \infty}}^{\infty}{\delta\left( {{J\quad\Omega} - u_{0}} \right)}}}} & (35)\end{matrix}$hence we obtain b_(L1) (equation 36): $\begin{matrix}{{b_{L1}} = {\frac{2}{\Omega}{{{\int_{{- \Omega}/2}^{\Omega/2}{{H^{+}(u)}\exp}} - {{\mathbb{i}}\quad\frac{2\pi\quad{Lu}}{\Omega}\quad{\mathbb{d}u}}}}}} & (36)\end{matrix}$

Now, at the second SLM define a periodic phase modulation G⁺(u), toobtain a_(−L2) (equation 37, 38): $\begin{matrix}{{\exp\quad i\left\{ {{{{kn}_{o}d} + {\phi_{C}(u)} + {{kd}\quad\theta_{INC}\frac{\partial n}{\partial\theta_{C}}}}❘_{\theta_{C}{(u)}}} \right\}} = {{G^{+}(u)}*{\sum\limits_{J = {- \infty}}^{\infty}{\delta\left( {{J\quad\Omega} - u_{l}} \right)}}}} & (37) \\{{a_{- {L2}}} = {\frac{2}{\Omega}{{{\int_{{- \Omega}/2}^{\Omega/2}{{G^{+}(u)}\exp}} + {{\mathbb{i}}\quad\frac{2\pi\quad{Lu}}{\Omega}\quad{\mathbb{d}u}}}}}} & (38)\end{matrix}$

Again, as we have already chosen that (equation 39)θ₂(u)=θ₁(−u)  (39)then, automatically, φ_(c)(u)=φ(−u), in which case G⁺(u)=H⁺(−u), andtherefore (equation 40)|b _(L1) |=|a _(−L2)|  (40)

Combining (36) and (40) we may obtain (equation 41):|a _(L1) ∥a _(−L2) |=|b _(L1) ∥b _(−L2)|  (41)

Hence, if the basic periodic patterns on the two SLMs are chosen tosatisfy (39), and the angle of incidence is such that the Poyntingvector of the light incident on the first SLM, and leaving the secondSLM, is in the plane of tilt of the director (in this case the x0zplane), the overall switch efficiencies can becomepolarisation-independent (equation 42):η_(OY)=η_(OXZ)  (42)

Note that this analysis neglects the change in beam direction betweenholograms due to diffraction-induced beam-steering. This may create somepolarisation-dependent loss, but it is expected that the configurationdescribed is still the optimum, as it cancels thepolarisation-dependence of the system as a whole due to the angle ofincidence.

Given that the two orthogonal components perceive different phasemodulation at each plane, the holograms must be designed that theworst-case unwanted diffraction orders do not cause unacceptablecrosstalk.

There have thus been described devices and systems for optical switchingwhich are polarisation insensitive. Embodiments of the invention asdescribed are capable of high performance in respect of cross talk.

1-30. (canceled)
 31. A reflective liquid crystal spatial light modulatorcomprising a transparent conductive layer, and a two dimensional arrayof pixels comprising a plurality of pixels; each pixel having arespective single reflective electrode, the reflective liquid crystalspatial light modulator further comprising a quarter wave plate disposedon the reflective electrodes, a liquid crystal layer disposed over thequarter wave-plate, and a transparent conductive layer over the liquidcrystal layer, wherein the transparent conductive layer forms a commonelectrode to said array.
 32. The reflective liquid crystal spatial lightmodulator of claim 31, wherein said liquid crystal layer is a nematicliquid crystal layer.
 33. The reflective liquid crystal spatial lightmodulator of claim 31, wherein said liquid crystal layer is a n-cell.34. An integrated spatial light modulator for light of a predeterminedwavelength, the integrated spatial light modulator comprising: atransparent common electrode, a plurality of reflective electrodes, aretardance layer having an optical retardance of an odd integer numberof quarter-waves of said predetermined wavelength, the retardance layerbeing disposed on the plurality of reflective electrodes; and a liquidcrystal layer, wherein the liquid crystal layer is disposed between theretardance layer and the transparent common electrode, wherein theliquid crystal layer is disposed and configured to provide out-of-planetilt in response to voltage applied across the liquid crystal layerbetween the reflective electrodes and the transparent common electrode;wherein the reflective electrodes are reflective pixel electrodesdisposed in a regular two-dimensional array.
 35. The integrated spatiallight modulator of claim 34, wherein said liquid crystal layer is anematic liquid crystal layer.
 36. The integrated spatial light modulatorof claim 34, wherein said liquid crystal layer is a n-cell.
 37. Theintegrated spatial light modulator of claim 34 further comprisingvoltage application circuitry for applying desired voltages across theliquid crystal layer whereby the liquid crystal layer has desired valuesof out of plane tilt; the arrangement being such that application ofvoltage to each electrode causes a respective portion of the liquidcrystal layer associated with a respective reflective pixel electrode tohave a specific value of said out-of-plane tilt; and wherein the voltageapplication circuitry is adapted to apply voltages to said twodimensional pixel array for two-dimensionally steering light incidentupon said modulator.
 38. A method of routing a light beam incident on anarray of phase modulating elements, the light beam having a firstcomponent polarized in a first direction and a second componentpolarized in a second direction orthogonal to the first, the methodcomprising: a) providing an integrated spatial light modulatorcomprising a liquid crystal layer, a wave plate layer having an opticalretardance of (2n+1) λ/4, a transparent conductive layer, and areflector layer, the liquid crystal being responsive to a variation in adrive voltage to provide a variation in out-of-plane director angletilt, the spatial light modulator having: a two dimensional array ofpixels; and an array of electrodes wherein each electrode is associatedwith a respective pixel of the integrated spatial light modulator and arespective portion of the liquid crystal layer to define a said phasemodulating element whereby the spatial light modulator comprises a saidarray of phase modulating elements; b) applying respective drivevoltages to each said electrode whereby the portion of liquid crystalassociated with the electrode has a respective specific value ofdirector angle tilt; c) applying said beam to the integrated spatiallight modulator whereby the first and second components each passthrough the liquid crystal layer and the wave plate layer, and arereflected at the reflector layer to again pass through the wave platelayer and liquid crystal layer to emerge with both components phasemodulated by the same amount; and d) controlling the drive voltages tovary a deflection direction of said light beam due to said array ofphase modulating elements.
 39. An optical switch comprising anintegrated spatial light modulator for light of a predeterminedwavelength, the integrated spatial light modulator comprising: atransparent conductive layer, a plurality of reflective pixelelectrodes, said reflective pixel electrodes being disposed in a regulartwo-dimensional array; a retardance layer having an optical retardanceof an odd integer number of quarter-waves of said predeterminedwavelength, the retardance layer being disposed on the regulartwo-dimensional pixel array; and a liquid crystal layer being disposedbetween the retardance layer and the transparent conductive layer. 40.The switch of claim 39, wherein said liquid crystal layer is a nematiccrystal layer.
 41. The switch of claim 40, wherein said liquid crystallayer is a n-cell.